Mendelson's Intro to Topology was a bit vague on what the complement of a cartesian product would be (and by a bit vague, I mean completely silent). I'm guessing that C(XxY) would = {(q1,w1),(q2,w2),...(qn,wn​)} where q is not in X and w is not in Y, yes?

I find this post almost unreadable. I know Bert's textbook very well having taught from it several times. You description is hard to follow. But this must be what it means: all of which must be in a larger space.

By definition means that .

So the negation is means that .

Now means , union.

So it is very clear means that

November 25th 2012, 05:56 PM

jakncoke

Re: Basic Set Theory (Cartesian Products): a simple exercise.

Lets see, if X and Y are sets, then is the set of all 2 tuples (x, y) where AND. Now the logical negation of the statement is . Which means that atleast one of the statements have to be true. So either or or and have to be true. So we have the union of 3 sets. The first case, if is true. Now it dosent matter where y is in, it can be anywhere in its universe, since the we only care about the statement . So the first cartesian product is . The next case is if is true. Then it does not matter where x is in its universe, which is A, so the second cartesian product is . Now the third case is if both statements are true. and . which means . So . Notice that So, we have only

November 25th 2012, 06:05 PM

MadMikey

Re: Basic Set Theory (Cartesian Products): a simple exercise.

Quote:

Originally Posted by Plato

I find this post almost unreadable.

I apologize, I don't yet know how to use the LaTex programming. I'll go check out the help forum.